Dominated polynomials on infinite dimensional spaces
Geraldo Botelho, Daniel Pellegrino, Pilar Rueda
TL;DR
This paper proves a stronger version of a conjecture regarding the existence of non-dominated scalar-valued m-homogeneous polynomials on infinite dimensional Banach spaces, advancing understanding in functional analysis.
Contribution
It establishes a more robust result confirming the existence of non-dominated polynomials in infinite dimensional Banach spaces, improving previous conjectures.
Findings
Confirmed the existence of non-dominated polynomials for m>=3
Provided a stronger version of the conjecture
Enhanced understanding of polynomial behavior in Banach spaces
Abstract
The aim of this paper is to prove a stronger version of a conjecture on the existence of non-dominated scalar-valued m-homogeneous polynomials (m>=3) on arbitrary infinite dimensional Banach spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Banach Space Theory · Holomorphic and Operator Theory · Fixed Point Theorems Analysis